This invention relates to the field of geophysical prospecting and, more particularly to methods for acquiring and processing seismic data.
In the oil and gas industry, geophysical seismic data analysis and processing techniques are commonly used to aid in the search for and evaluation of subterranean hydrocarbon deposits. Generally, a seismic energy source is used to generate a seismic signal that propagates into the earth and is at least partially reflected by subsurface seismic reflectors (i.e., interfaces between underground formations having different acoustic impedances). The reflections are recorded in a geophysical time series by seismic detectors located at or near the surface of the earth, in a body of water, or at known depths in boreholes, and the resulting seismic data may be processed to yield information relating to the location of the subsurface reflectors and the physical properties of the subsurface formations.
Seismic or acoustic energy may be from an explosive, implosive, swept-frequency (chirp) or random source. A geophysical time series recording of the acoustic reflection and refraction wavefronts that travel from the source to a receiver is used to produce a seismic field record. Variations in the travel times of reflection and refraction events in these field records indicate the position of reflection surfaces within the earth. The analysis and correlation of events in one or more field records in seismic data processing produces an acoustic image that demonstrates subsurface structure. The acoustic images may be used to aid the search for and exploitation of valuable mineral deposits.
These seismic data are processed to be useful for delineating features in the earth""s subsurface. Geophysical time series data acquired in the field often contain unwanted energy as well as desired energy. Some of the unwanted energy may interfere with, overwhelm or otherwise mask desired seismic energy useful for subsurface investigations. There are many known methods for filtering or separating unwanted energy from seismic signals.
Prior art processing methods for eliminating unwanted energy include frequency filtering, windowed frequency filtering, and f-k filtering. Filtering may be applied to each trace individually or to multiple traces concurrently. Elimination of unwanted energy traditionally results from the application of filtering to entire traces regardless of whether the unwanted energy is localized in only part of the data trace.
Traditional filtering is usually implemented in frequency-time space using orthogonal basis functions having perfect localization in frequency but infinite extent in time. Use of the Fourier transform is well known in the art and the most common type of filtering for geophysical data. The underlying assumption of this type of filtering is that the seismic signals are stationary (e.g., do not have time dependent statistical characteristics). However, it is well known in the art that many types of seismic signals recorded in the field are non-stationary. It would be beneficial to filter geophysical time series data containing unwanted non-stationary energy without adversely impacting desired seismic signal.
An alternative to the Fourier transform is the continuous wavelet transform (CWT). In the continuous wavelet transform, a function "psgr" is used to create a family of wavelets "psgr" (at+b) where a and b are real numbers, a dilating the function "psgr" and b translating the function. The CWT turns a signal f(t) into a function with two variables (scale and time), which may be called c(a,b) such that c(a,b)=∫f(t)"psgr"(at+b)dt. The CWT allows for joint time-frequency localization ideal for non-stationary filtering. The discrete wavelet transform (DWT) is a special case of the CWT.
Wavelet methods may be designed in transform space rather than data space. However, as is evident from comparing FIG. 2A, data prior to transformation, with FIG. 2B, data from the same seismic record after transformation with wavelet methods, the wavelet transform alters coordinate relationships in the original geophysical time series data ensemble. This altered coordinate relationship is due to an inescapable limitation on joint time-frequency resolution imposed by the transform technique. Though the transformed data contains the required non-stationary time-frequency signal characteristics, signal components are difficult to recognize from their original space-time geometry. To address this dilemma, some practitioners have developed graphing techniques to approximately restore original data-space coordinate relationships to the transformed signals. The details of the technique depend on the particular choice of transform. Deighan and Watts (1997) give an example for a wavelet transform in FIG. 6 of their paper. (GEOPHYSICS, VOL. 62, NO. 6, NOVEMBER-DECEMBER 1997; P. 1896-1903) U.S. Pat. No. 5,781,502 to Becquey proposes a method to discriminate elliptical waves propagating in a geologic formation by a combined process that includes measuring and comparing ratios of components along several wave axes. The method calls for the use of multi-component seismic data. The method is directed to removing elliptical waves from seismic data after wavelet analysis is used to determine the surface or tube waves in the data. The detected signals are subtracted from the field records.
U.S Pat. No. 5,850,622 to Vassiliou et al. disclose a method to filter seismic data using very short-time Fourier transforms. The method utilizes a very great number of short overlapping Fourier transform windows, together with a Gaussian weight or taper function, to produce a plurality of near single-frequency xe2x80x9csub-bandxe2x80x9d traces for each seismic trace so analyzed. The transformed data may be used for selective removal of coherent noise events, analysis for seismic attributes related to subsurface features of interest, seismic trace creation by interpolation, and automatic identification and removal of noisy seismic traces.
A method of designing and applying filters for geophysical time series data is described which comprises obtaining a plurality of spatially related geophysical time series and transforming the time series using a wavelet transformation. The wavelet transformation coefficients may be organized into a plurality of subband traces. The method includes modifying one or more transform coefficients within a plurality of the subband traces or within all but one of the subbands of traces and then inverting the subband traces using an inverse transform to produce a filtered version of the transformed portion of the geophysical time series. The method allows for design and analysis of non-stationary filters and filter parameters in untransformed data space. Non-stationary signals may be filtered in all or in windowed portions of the geophysical time series data.